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Real world data often exhibit low-dimensional geometric structures, and can be viewed as samples near a low-dimensional manifold.
Nonlinear approximation and (deep) relu networks
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Deep relu network approximation of functions on a manifold
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Multilayer feedforward networks with a nonpolynomial activation function can approximate any function
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A distribution-free theory of nonparametric regression
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Hinton, G. E · 2006
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Lee, J. M · 2006
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Wasserman, L · 2006
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Local polynomial regression on unknown manifolds
Bickel, P. J · 2007
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The mathematical theory of finite element methods
Minimax-optimal nonparametric regression in high dimensions
Yang, Y · 2015
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Amodei, D · 2016
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Deep nets for local manifold learning
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Deep learning
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Brenner, S · 2007
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Relu nets adapt to intrinsic dimensionality beyond the target domain
Cloninger, A · 2008
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Finding the homology of submanifolds with high confidence from random samples
Niyogi, P · 2008
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Introduction to nonparametric estimation
Tsybakov, A. B · 2008
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Rectified linear units improve restricted boltzmann machines
Nair, V · 2010
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An introduction to manifolds
Tu, L · 2010
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Hanin, B · 2017
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Artificial intelligence in healthcare: past, present and future
Jiang, F · 2017
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The expressive power of neural networks: A view from the width
Lu, Z · 2017
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Deep learning for healthcare: review, opportunities and challenges
Miotto, R · 2017
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Low dimensional manifold model for image processing
Osher, S · 2017
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Nonparametric regression using deep neural networks with relu activation function
Schmidt-Hieber, J · 2017
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Error bounds for approximations with deep relu networks
Yarotsky, D · 2017
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Squeeze-and-excitation networks
Hu, J · 2018
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Fast convergence rates of deep neural networks for classification
Kim, Y · 2018
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Introduction to Riemannian manifolds
Lee, J. M · 2018
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Provable approximation properties for deep neural networks
Shaham, U · 2018
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Recent trends in deep learning based natural language processing
Young, T · 2018
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Estimating the reach of a manifold
Aamari, E · 2019
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Efficient approximation of deep relu networks for functions on low dimensional manifolds
Chen, M · 2019
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Smooth function approximation by deep neural networks with general activation functions
Ohn, I · 2019
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Adaptivity of deep reLU network for learning in besov and mixed smooth besov spaces: optimal rate and curse of dimensionality
Suzuki, T · 2019
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Universality of deep convolutional neural networks
Zhou, D.-X · 2019
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Error bounds for approximations with deep relu neural networks in w s , p w^{s,p} norms
Gühring, I · 2020
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Adaptive approximation and generalization of deep neural network with intrinsic dimensionality
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Multiscale regression on unknown manifolds
Liao, W · 2021
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